The Pythagorean Theorem

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The Pythagorean Theorem

• From The Simpsons Homer copies the Scarecrow on
  The Wizard of Oz.

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The Pythagorean Theorem

• The sum of the square of the two sides of a right
  triangle is equal to the square of the
  hypotenuse.

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The sum of the square of the two sides of a right
triangle is equal to the square of the
hypotenuse.
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An example of the Pythagorean Theorem

• Let the adjacent side of the right triangle be 10
  and the opposite side be 12. Find the hypotenuse
  of the right triangle.

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Now you try it!

• Let the adjacent side of the right triangle be 12
  and the hypotenuse be 13. Find the opposite side
  of the right triangle.

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Definition of the Trig. Functions
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An example of the Trigonometric Functions

• Let the adjacent side of the right triangle be 10
  and the opposite side be 12. Find all the
  trigonometric functions of the given angle theta.

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Now you try it!

• Let the adjacent side of the right triangle be 12
  and the hypotenuse be 13. Find all the
  trigonometric functions of the given angle theta.

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Special Angles and Trig. Functions

• The 30-60-90 triangle

Thus the 30-60-90 triangle sides are in the
ratio of 1 - - 2.
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Trig. Functions of 30-60-90 triangles.
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Special Angles and Trig. Functions

• The 45-45-90 triangle

Thus the 45-45-90 triangle sides are in the
ratio of 1 - 1 - .
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Trig. Functions of 45-45-90 triangles.
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The Unit Circle
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The Unit Circle